You don't need to swap the cabin harnesses, the engine harness is separate from the other harnesses (one thing I love about 240s is their modularity).
So you'd have to separate the transmission to swap the flywheel or flex plate for the toothed 2.4 version and mount the crank position sensor
Then you would swap the whole engine wiring harness and the ECU (fuel computer). I forget if 2.2 240s already have an EZK (ignition computer), if they do then you can leave that alone.
You also need to swap the engine coolant temp sensor and the AMM.
The distributors are different, but you can leave the LH-2.2 distributor as-is, it just won't have anything plugged into it from the harness anymore.
My only advice if you pull the harness is do not cut any wires, pull the whole engine harness intact. This includes the cable bundle that runs inside the cabin, along the firewall from the passenger side to where the ECU mounts to the right of the driver's feet.
The interior trim panels and brackets that cover the ECU are handy to have. The EZK mounts to a bracket on the cabin side of the firewall near where the loom passes into the cabin from the engine bay.